时滞细胞神经网络的时滞相关指数稳定性

应用Lyapunov泛函法研究了具有时滞的细胞神经网络（DCNNs）的平衡点的全局指数稳定性，获得了一个指数稳定性的判定准则。这个准则与时滞的大小有关，即DCNNs是指数稳定的只要系统所含时滞不超过一个界。     

具有时滞的细胞神经网络的全局指数稳定性

利用Liapunov函数方法,结合积分不等式技巧,分析了时滞细胞神经网络的平衡点存在的唯一性和全局指数稳定性,保证时滞细胞神经网络全局指数稳定的一个新的充分判据被得到.所得判据比已有文献具有更少的限制,为实际应用提供了方便.     

具有分布时滞和区间参数的随机系统的p-阶矩指数鲁棒稳定性

研究了一类具有分布时滞和区间参数的随机系统的p-阶矩指数鲁棒稳定性问题,利用Liapunov-Krasovskii泛函、区间矩阵的分解技术及Ito公式,得到了该系统p-阶矩指数鲁棒稳定的时滞依赖的稳定性判据.通过数值例子说明了所得判据的有效性和实用性.     

具有脉冲效应的灰色随机时滞系统的鲁棒稳定性

研究了一类具有脉冲效应和时变时滞的灰色随机系统的鲁棒稳定性问题。在给出了脉冲随机泛函微分系统随机稳定性的条件的基础上,首先利用Lyapunov-KrasoVskii泛函法和灰矩阵的连续矩阵覆盖的分解技术,得到了具有脉冲效应和时变时滞的灰色随机系统的随机鲁棒稳定性判据,进而基于所得的这个随机鲁棒稳定性判据和Dini导数,给出了该系统指数鲁棒稳定性的判据。实例表明,所得判据是有效的和实用的。     

一类区间随机分布时滞系统的p-阶矩指数稳定性

研究了一类区间随机分布时滞系统的p-阶矩指数稳定性问题.利用分布时滞转化为点时滞方法和区间矩阵的分解技术,得到了该系统p-阶矩指数稳定的时滞依赖的稳定性判据.通过数值例子说明了所得判据的有效性和实用性.     

变时滞细胞神经网络稳定性分析

利用矩阵测度、Liapunov函数和Halanay时滞不等式的方法研究了具有变时滞的细胞神经网络模型平衡点的全局指数稳定性问题.给出了判定平衡点全局指数稳定性的几个代数判据,可用于时滞细胞神经网络的设计与检验,数值算例说明其结果的优越性.     

带有时变时滞的中立型神经网络的鲁棒指数稳定性

研究一类带有时变时滞的中立型神经网络的全局指数稳定性问题.通过构造LyapunovKrasovskii泛函并使用线性矩阵不等式方法,建立了保障时滞神经网络全局指数稳定的新的时滞相关充分条件.这些条件用线性矩阵不等式表达.进一步,文章对一类不确定时滞中立型神经网络给出了鲁棒全局指数稳定的新判据.     

具有参数不确定性的线性中立型时变时滞系统的鲁棒稳定性

本文研究一类具有参数不确定性的线性中立型时变时滞系统的鲁棒稳定性.首先,利用Jensen’s不等式,并采用新方法来处理积分项,得到标称中立型系统的稳定性判据.然后,基于标称系统的稳定性结果,进一步得到系统矩阵存在不确定性时的鲁棒稳定性判据.本文的新方法能充分利用负定项的信息,故稳定性结果的保守性更低.最后,两个数值例子分别验证了文中所得的标称中立型系统稳定性判据的保守性更低,以及系统矩阵存在不确定性时的鲁棒稳定性判据的可行性.     

变时滞Hopfield神经网络的周期解存在性及其全局指数稳定性

利用拓扑度理论中的连续性引理和推广Halanay不等式研究了变时滞的细胞神经网络的周期解的存在性及全局指数稳定性.给出了判别周期解及指数稳定性的代数判据,所得判据易于检验,具有广泛的实用性．同时,改进了已有文献的相关结论,最后通过数值例子说明结论的有效性．     

具有分布时滞的灰色随机非线性系统的鲁棒稳定性

利用灰矩阵的矩阵覆盖集的分解技术和矩阵的范数理论及Lyapunov-K rasovsk ii泛函法,研究了具有分布时滞的灰色随机非线性系统的鲁棒稳定性问题,得到了该系统鲁棒稳定的时滞依赖的线性矩阵不等式(LM Is)判据,并通过数值例子说明了所得的"LM Is判据"的有效性和实用性.     

对延迟细胞神经网络全局渐近稳定性一个结果的改进

给出了延迟细胞神经网络全局渐近稳定性的一个新的充分条件,该条件改进并推广了已有文献中的结论.     

Global robust stability of interval cellular neural networks with time-varying delays

This paper studies the global robust asymptotic stability (GRAS) and global robust exponential stability (GRES) of delayed cellular neural networks with time-varying delays. A series of new criteria concerning GRAS and GRES are obtained by employing the Young's inequality, Halanay's inequality and Lyapunov functional and combine with some analysis techniques. Several previous results are improved and generalized. Some examples and remarks are also given to illustrate the effectiveness of the results. In addition, these criteria possess important leading significance in design and applications of global stable DCNNs, and are of great interest in many applications.     

Delay-dependent exponential stability for a class of neural networks with time delays

This paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type. In terms of a linear matrix inequality (LMI), a sufficient condition guaranteeing the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed. This condition is dependent on the size of the time delay, which is usually less conservative than delay-independent ones. The proposed LMI condition can be checked easily by recently developed algorithms solving LMIs. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.     

Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays

In this paper, the global robust exponential stability for a class of delayed BAM neural networks with norm-bounded uncertainty is studied. Some less conservative conditions are presented for the global exponential stability of BAM neural networks with time-varying delays by constructing a new class of Lyapunov functionals combined with free-weighting matrices. This novel approach, based on the linear matrix inequality (LMI) technique, removes some existing restrictions on the system’s parameters, and the derived conditions are easy to verify via the LMI toolbox. Comparisons between our results and previous results admit that our results establish a new set of stability criteria for delayed BAM neural networks.     

一类扩张的细胞神经网络稳定性判别法

本文研究一类含有阻尼项带有时滞细胞神经网络的全局渐进稳定性和一致稳定性的性质,通过构造适当的李雅普诺夫函数及利用分析的有关知识,给出了全局渐进稳定性和一致稳定的判别法．     

Delay-dependent global asymptotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters

This paper investigates the delay-dependent global asymptotic stability problem of stochastic genetic regulatory networks (SGRNs) with Markovian jumping parameters. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are globally asymptotically stable in the mean square. Distinct difference from other analytical approaches lies in “linearization” of the genetic regulatory networks (GRNs) model, by which the considered GRN model is transformed into a linear system. Then, a process, which is called parameterized first-order model transformation is used to transform the linear system. Novel criteria for global asymptotic stability of the SGRNs with constant delays are obtained. Some numerical examples are given to illustrate the effectiveness of our theoretical results.     

Mean square global asymptotic stability of stochastic recurrent neural networks with distributed delays

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability in the mean square of delayed neural networks.     

A new global stability result for delayed neural networks

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new sufficient condition is presented for the global asymptotic stability of delayed neural networks. The condition contains and improves some of the previous results in the earlier references.     

Delay-dependent global stability condition for delayed Hopfield neural networks

In this paper, by utilizing the Lyapunov functional method and combining with the linear matrix inequality approach, we analyze the global asymptotic stability of delayed Hopfield neural networks (HNNs). A new sufficient condition ensuring the global stability of the unique equilibrium point of delayed HNNs is obtained, which is dependent on the size of delays. This condition is less restrictive and conservative than that given in the earlier references. In addition, an example is also provided to illustrate the applicability of the result.     

New results on global asymptotic stability analysis for neural networks with time-varying delays

This note provides new results on global asymptotic stability for neural networks with time-varying delay. Two types of time-varying delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing an augmented Lyapunov–Krasovskii functional, new delay-dependent stability criteria for delayed neural networks are derived in terms of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.